Conventionally, for an engine that incorporates a hydraulically operated variable valve mechanism (hereinafter, abbreviated as “hydraulic VTC mechanism”), a control gain for estimating an oil pressure based on an engine speed, a temperature of cooling water, etc., and driving the hydraulic VTC mechanism is set. However, when a variable displacement pump, for example, an electronic two-stage hydraulic control pump (also called as “electronic VDVP, or two-stage oil pump when oil is supplied by) is used for supplying oil, hysteresis characteristics are imparted to switching of supply characteristics so that hunting of solenoid is suppressed. For this reason, even at the same engine speed or at the same temperature of cooling water, oil temperatures may be different from an estimated temperature. Thus, a responsiveness and a controllability which are expected for the hydraulic VTC mechanism are not necessarily obtained. Therefore, for example, Patent Document 1 teaches maintaining control stability by switching a target phase under a low hydraulic pressure.